This article presents the consensus of an National Council on Measurement in Education Presidential Task Force on Foundational Competencies in Educational Measurement. Foundational competencies are those that support future development of additional professional and disciplinary competencies. The authors develop a framework for foundational…

Item Response Theory models with varying thresholds are essential tools to account for unknown types of response tendencies in rating data. However, in order to separate constructs to be measured and response tendencies, specific constraints have to be imposed on varying thresholds and their interrelations. In this article, a multidimensional…

As simple and ubiquitous redox-active organic molecules, quinones participate in diverse electron transfer processes in chemistry and biological systems for energy transformation and signal transduction. We introduce here a practical exercise to study the redox potentials of benzoquinone and its two derivatives by combining the electrochemistry…

Quadratic functions are explained in the three equivalent formats: Standard (or Expanded), Vertex and Factorised. However, cubic functions are represented only in the two equivalent formats: Standard (or Expanded) and Factorised. In this article, the author shows how cubic functions can be expressed in three equivalent formats like quadratic…

An unplugged approach to teaching enables students to explore Computational Thinking without using a computer. It might appear that if students are to learn programming, they should focus on computer-based work; however, it appears that using "unplugged" activities before engaging in computer-based coding (programming) activities for…

Having students solve shape puzzles, such as with pattern blocks or tangrams, is a popular way to encourage students to compose shapes in different ways and talk about the effects of different compositions (Clements et al., 2004; Clements & Sarama, 2009; Sales, 1994), meeting Common Core geometry standards in kindergarten through second grade…

The introduction of Computational Chemistry via "Molecular Modelling and Drug Design" course at undergraduate level has opened wide possibilities for students to expand their knowledge of quantum chemistry, organic reaction mechanisms, protein-ligand interactions, drug design, and probable "in vivo" behavior of drug candidates.…

This review describes a computational chemistry exercise aimed at enhancing the understanding of upper-division undergraduates in organic chemistry and physical chemistry regarding the structures and aromaticities of cyclobutadiene and cyclooctatetraene. This exercise exposes students to chemical problems that require computational methods as a…

In this article the author describes an intervention program for students who were approximately six months behind expected standards. The program, "Prepare 2 Learn," had four components: building prior knowledge; developing mental computational fluency; encouraging a growth mindset; and meta-cognitive strategies. The qualitative data…

Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to…

A computational experiment investigating common organic chemistry mechanisms has been developed and implemented in a junior/senior-level physical chemistry laboratory course at two institutions. Students investigated various reactions that proceed via S[subscript N]1, S[subscript N]2, E1, and E2 mechanisms using hybrid Density Functional Theory…

Solution equilibria diagrams are excellent tools for understanding chemical speciation in multireaction chemical systems. They are usually plotted using software packages that efficiently perform advanced calculations, giving the possibility to graphically visualize thermodynamic and composition information. However, this approach frequently…

Pre literacy skills in young children have been well established. Explorations of the parallel concept of pre mathematic skills in young children are minimal. Recommendations for how to engage young children, specifically infants, in math have been limited to caregiver counting games. This colloquium presents an example of how an 11-month-old is…

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…